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Confidence intervals for long-horizon predictive regressions via reverse regressions

  • Min Wei
  • Jonathan Wright
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Long-horizon predictive regressions in finance pose formidable econometric problems when estimated using the sample sizes that are typically available. A remedy that has been proposed by Hodrick (1992) is to run a reverse regression in which short-horizon returns are projected onto a long-run mean of some predictor. By covariance stationarity, the slope coefficient is zero in the reverse regression if and only if it is zero in the original regression, but testing the hypothesis in the reverse regression avoids small sample problems. Unfortunately this only allows us to test the null of no predictability. In this paper we show how to use the reverse regression to test other hypotheses about the slope coefficient in a long-horizon predictive regression, and to form confidence intervals for this coefficient. We show that this approach to inference works well in small samples.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2009-27.

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Date of creation: 2009
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Handle: RePEc:fip:fedgfe:2009-27
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  1. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-79, June.
  2. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
  3. Graham Elliott & James H. Stock, 1992. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," NBER Technical Working Papers 0122, National Bureau of Economic Research, Inc.
  4. Campbell, John, 2000. "Asset Pricing at the Millennium," Scholarly Articles 3294737, Harvard University Department of Economics.
  5. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  6. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  7. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 2001. "Peso problem explanations for term structure anomalies," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 241-270, October.
  8. John Y. Campbell, 1993. "Why Long Horizons: A Study of Power Against Persistent Alternatives," NBER Technical Working Papers 0142, National Bureau of Economic Research, Inc.
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